Corrected entry: How was Nick able to save the little girl while still dying himself? We know that when he saved the boy the first time the day happened, he became trapped when the floor below him collapsed, and he told the boy to go on without him. Tru told him about the floor the second time, so he and the boy made it out safely. Then Nick went back in for the girl, and all we know is that the girl was saved and he still died. There is no explanation of what happened to somehow kill him after he saved the girl.
Corrected entry: The second time Tru goes through the day, she says that the fire truck will be delayed by traffic (she saw the flooded fire hydrant the first time), and realizes that's why Nick had to go into the building without his equipment. But the fire truck is actually there by the time they get outside.
Correction: But the problem was that they weren't there by the time he had to go inside. When he gets out on the second day it is already past the time he got stuck on the first day, so there's no problem there. On the second day he rushes back in too stubborn to wait - the other firefighters will physically stop Tru but not one of their own.
Corrected entry: On the second walk through of the day, Tru describes the fire (which hasn't happened yet) to Davis. From this description, Davis (who, bear in mind, is the supervisor at a morgue and not a criminal forensics expert) is able to provide more accurate information about the fire and its cause than were the emergency workers who brought the bodies to the morgue the first day, several hours after the fire actually happened, by which time some actual police investigation had presumably occurred as well.
Correction: Davis is an MD and performs autopsies as part of his job, so would be very familiar with the forensics, the morgue is directly beneath the sheriff's office after all. The people bringing the bodies in are not emergency workers, they work directly for the morgue, and Marco stated earlier that he just picks up the bodies he doesn't solve crimes, so he wouldn't have gotten that much information from the police.
Corrected entry: When Tru has lunch with Harrison the second time she goes through the day, she tells him that it will rain at three. This is information she presumably has from the first iteration of the day. Three o'clock passes without comment, and without rain.
Correction: We don't actually see three o'clock on either day. A short summer rain would leave no evidence after an hour or so, and wouldn't be worth discussing, especially with a building burning down at five o'clock.
Corrected entry: The first time Tru goes through the day, there is a scene with her and Meredith unpacking glassware. The scene serves only to provide exposition about Tru's mother. But why are they unpacking glassware in a house that appears to be newly moved into? We haven't been told about anybody moving into a new house, and there's no reference to moving or the glassware before or after. It doesn't fit in properly at all.
Correction: Somebody moved, or bought new glassware, and we don't know who. This doesn't really seem like a mistake, just leaving out information that isn't really that important to the story.
Correction: The is no explanation given in the episode but there are plenty of possible explanations of how someone could die in a burning building without any protective gear.